Ioan,
Your prop vs engine comparison is a perfect illustration of what I said, the air mover stuff has made small strides while the engine power to weight has made amazing strides. This is because the prop/rotors are merely converting momentum, a fairly low-tech task. Engines do amazing backflips to convert chemical energy into power.
The Wright engine was very heavy relative to today's numbers, but it was about 10 times the weight efficiency of anything that had previously been made. It was a wonder, but it was 100 times heavier than the engine in a Black Hawk, per horsepower.
mini,
The typical turbine is inefficient in terms of power to fuel burn when compared to a piston. Efficiency is almost purely driven by the internal temperature that the engine produces, because the most efficient engine has a big delta temp from its power cycle to the outside (so therefore there is a big "natural" heat rejection that is the thermodynamic equivalent of voltage, a big push for each package of hot gas).
A turbine usually is operated at lower power and temperatures to allow long life, and also to keep the highest power (and temperature) in reserve for emergencies. Pistons burn their fuel at the hottest temp all the time (they can because their valves are tucked into the head to conduct away heat and shield them from the hottest temps), and they increase their power output by increasing rpm to process more fuel per second.
Some numbers:
a good turbine burns .6 to .8 lbs of fuel per hour per HP in cruise, and .5 to .6 at takeoff (more efficient)
A regular piston engine burns about .41 to .47 lb/hp/hr
source:
http://www.jet-engine.net/civtsspec.html
http://en.wikipedia.org/wiki/Specific_fuel_consumption